If a hitch head is shifting, the bolts are not tight enough. Get the head in the position it needs to be and tighten it to proper torque. If the head moves when you load and unload it with the bars you can bet it is, "working", as you go down the road and the whole unit bounces and flexes. If the hitch head is moving on the mount, it will wear and move more. I expect it will, eventually, break the bolts.
I would not take my truck to a tire shop that just runs the lug nuts up with an impact wrench. They are not only, probably stretching the bolts and weakening them, you will never get the wheel off with a lug wrench if you have a flat.
I always watch when I have tire work done to be sure it's done properly. I have prevented installers from putting a floor jack under the center of my TT axle and explained to them how to lift it right. My tire shop runs the lug nuts up close with the air wrench and then takes a torque wrench and does each one to the proper torque and then rechecks them again.